The segmented coronagraph design and analysis (SCDA) study is a coordinated effort, led by Stuart Shaklan (JPL) and supported by NASA’s Exoplanet Exploration Program (ExEP), to provide efficient coronagraph design concepts for exoplanet imaging with future segmented aperture space telescopes. This document serves as an update on the apodized vortex coronagraph designs devised by the Caltech/JPL SCDA team. Apodized vortex coronagraphs come in two flavors, where the apodization is achieved either by use of 1) a gray-scale semi-transparent pupil mask or 2) a pair of deformable mirrors in series. Each approach has attractive benefits. This document presents a comprehensive review of the former type. Future theoretical investigations will further explore the use of deformable mirrors for apodization.